I haven't seen any formulae for this. The effect should be similar, but smaller, than increasing the track thickness, for which there are formulae. It will increase the small capacitance of the edges of the microstrip and of the very small capacitance of the top of the microstrip.

See https://www.researchgate.net/post/Does_Microstrip_thickness_matters_in_impedance

Malcolm White Thanks for your kindly reply.

I can image the how qualitatively solder masks affect the impedance.

But I want to know how to quantify it approximately.

Please see

https://ieeexplore.ieee.org/document/127530

https://www.emerald.com/insight/content/doi/10.1108/COMPEL-10-2012-0283/full/html

They all did a good job when it comes to the thin strip case of the microstip line with solder mask

However, I want to find a more general one which consider the finite thickness of the strip just like what Wheeler did.

Thank you!

I guess when saying impedance formula you have the characteristic impedance in mind. For this kind of quasi TEM lines (hybrid modes) there exist different definitions of the characteristic impedance (e.g. voltage/current..power/voltage.. power current).I presume one can find some papers on this subject via IEEE explore..

Fritz Caspers

Thanks for your comments.

Even for quasi-TEM modes in transmission lines, before cutoff frequency, I guess people always like to use RLGC to represent the characteristic impedance. Could you please give me some examples of different definitions of the characteristic impedance? I didn't see that.

For the question I asked above, I always found the characteristic impedance of three dielectric transmission lines without thickness-correction just like these two papers:

Article Analysis of Multilayer Microstrip Lines by a Conformal Mapping Method

https://www.emerald.com/insight/content/doi/10.1108/COMPEL-10-2012-0283/full/html

If you have any idea for that, please tell me.

Thank you!

you can find the discussion and comparison for the different definitions of the char. impedance in the book by R.K Hoffman "integrated microwave circuits".

Springer 1983 ISBN 3-540-12352-0

I have only the german edition at hand and there its on page 132...

(just to repeat it here: current-voltage definition; power-current definition; and power-voltage definition)

I have found by chance exactly this structure discussed in the "transmission line design handbook" by Wadell on page 116..including some references; there are several names in the literature such as: microstrip with dielectric overlay; Dielectrically shielded microstrip line; Microstrip line with two dielectrics.

Fritz Caspers

Wadell's book is outstanding for its collections of formulae of several types of the characteristic impedance.

However, I've read it before asking the question and the related articles of my questions doesn't give me the answer. I think the reason may comes from the first analytic form of the characteristic impedance of the microstrip line for three dielectric case, so far I've seen, is published after the publication of this book.

For now, owning to the thin strip for microstrip line in three dielectric case discussed only, my questions are turned into that the wheeler' finite-thickness correction holds even in the microstrip line in the multi-dielectric case or not.

Thanks for your kindly discussing!

Fritz Caspers

Malcolm White

Eventually, I found that the following combination is the best.

Wheeler's microstrip line impedance with air loaded + Wheeler's thickness correction + Svacina's effective dielectric constant

At least, this set is proper for the PCB interconnect, where the operation frequency is not high compared to RF.

For the end of this discussion, I just wanted to share to you.

Thinks for your kind replies to my questions :)

In this case case I would go for a numerical evaluation which is rather easy these days..even if there is a formula somewhere it will be an approximation and not straightforward to solve

Fritz Caspers

You are right.

It's for sure that simulation is the most precise one but it takes time.

(But maybe, for 2D simulation, it is not time-consuming)

The equation helps to quickly evaluate something.

Hence, it still needs to explore such an approximation.

Also, in the company, one usually needs the commercial software to do that, and such an approximation can be used to escape the license issue. XD

Anyway, I appreciate your comment so much.

Thanks

Just keep in mind that for this kind of structure you dont have a TEM mode but rather something like a quasi or pseudo TEM mode (or hybrid mode) since the propagation velocity (for a true TEM wave) on the different parts would not be equal. This leads to longitudinal field components..and thus hybrid modes where also the definition of the char. impedance is not unambigous.